Partiality and Games: Propositional Logi
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Partiality and Games: Propositional Logic
We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic p...
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The Logi of Proofs LP solved a long standing Godel's problem onerning his provability al ulus ( f. [4℄). It also opened new lines of resear h in proof theory, modal logi , typed programming languages, knowledge representation, et . The propositional logi of proofs is de idable and admits a omplete axiomatization. In this paper we show that the rst order logi of proofs is not re ursively axioma...
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